Multi-Scale Turing Patterns

Multi-Scale Turing Patterns is a live web notebook that implements the Cyclic Symmetric Multi-Scale Turing Patterns algorithm of Jonathan McCabe using WebGPU. The tool simulates activator-inhibitor dynamics across multiple spatial scales, producing complex generative patterns by leveraging FFT-based convolution with analytical kernels such as Gaussian and circular. The notebook translates previous implementations of this algorithm to a WebGPU-powered environment, allowing for interactive exploration and visualization of the resulting patterns.

A key feature of this tool is its parameterization of pattern scales. Users can adjust activator radius, inhibitor-to-activator ratio, kernel shape, step size multiplier, weight, and symmetry order for each scale. These parameters influence the detail, separation, and symmetry of the generated patterns, enabling the creation of a wide variety of visual effects. The algorithm determines, at each point, which scale has the minimum variation, and blends colors based on local dominance, resulting in the characteristic multi-scale appearance. Interactive controls allow users to zoom and pan the visualization, and a fullscreen mode is available for more immersive viewing.

The notebook also includes an implementation of the Gray-Scott reaction-diffusion model, providing background on the mathematical foundations of pattern formation. It discusses the derivation of bifurcation curves and the stability of steady states, as well as the principles of the activator-inhibitor model first proposed by Alan Turing. This makes the tool suitable not only for visual experimentation but also for educational purposes, particularly for those interested in mathematical modeling, pattern formation, or generative art.

Multi-Scale Turing Patterns is accessed through a web interface and is aimed at users interested in exploring reaction-diffusion systems and multi-scale pattern generation.